Dynamics of Sunspot Series on Time Scales From Days to Years: Correlation of Sunspot Births, Variable Lifetimes, and Evolution of the High‐Frequency Spectral Component

• Published in: Journal of geophysical research. Space physics 2017-12, Vol.122 (12), p.11,874-11,887
• Main Authors: Shapoval, A., Le Mouël, J.‐L., Shnirman, M., Courtillot, V.
• Format: Article
• Language: English
• Subjects: autoregression; Autoregressive models; Autoregressive processes; Birth rate; Birthrate; Dynamo theory; Evolution; lifetime; Solar activity; Solar cycle; Sunspot groups; Sunspot numbers; Sunspots
• ISSN: 2169-9380; 2169-9402
• DOI: 10.1002/2017JA024430

This paper explores some features of the dynamics of daily sunspot numbers on scales from days to years. We define higher and lower frequency energy components of the series that are related to periods ranging over 1 to 6 days and 6 days to 2 years, respectively. The lower frequency component is found to follow the solar activity, but the maxima of the higher frequency component are unexpectedly lower during the last epoch of high solar activity than during the preceding epoch of low solar activity. We also consider the birthrate of sunspot groups as another indicator of quickly varying components of the solar activity and show that it is the general growth of solar activity in the 1930–1940s that drives up this birthrate. We propose an autoregressive model that captures the opposite trends exhibited by the two representatives of the high‐frequency content, accurately reproduces the evolutions of the lower and higher frequency energy components, and replicates the shape of the curve representing the daily sunspot numbers. The three following hypotheses underlie the model construction: (1) proxy series of solar activity can be modeled by a random process with a modulated noise; (2) sunspot's birth and disappearance rates, both following the solar cycle, determine properties of this process; and (3) the births of sunspots are positively correlated in time during epochs of high solar activity. We find that the mean birthrate varies as a power function of the mean lifetime. Derived constraints could contribute to narrowing the choice of a proper solar dynamo model. Key Points Sunspot numbers' spectral component corresponding to the range of 1–6 day periods decreased when solar activity increased in the 1940s An order 1 autoregressive process with modulated noise replicates the evolution of daily sunspot number series and its spectrum The relationship between the average lifetime and average birthrate of sunspots is described by a power function